Robust Online and Distributed Mean Estimation Under Adversarial Data Corruption

TL;DR

This paper introduces robust online and distributed algorithms for mean estimation in adversarial settings, ensuring convergence despite data corruption, with analysis of network topology effects on convergence rates.

Contribution

The paper presents novel algorithms for robust mean estimation in online and distributed environments with adversarial data, including error bounds and convergence analysis.

Findings

Algorithms achieve asymptotic convergence to the true mean.

Error bounds are established for the estimation process.

Network topology influences the convergence rate and trade-offs.

Abstract

We study robust mean estimation in an online and distributed scenario in the presence of adversarial data attacks. At each time step, each agent in a network receives a potentially corrupted data point, where the data points were originally independent and identically distributed samples of a random variable. We propose online and distributed algorithms for all agents to asymptotically estimate the mean. We provide the error-bound and the convergence properties of the estimates to the true mean under our algorithms. Based on the network topology, we further evaluate each agent's trade-off in convergence rate between incorporating data from neighbors and learning with only local observations.